Consider the two-module configuration of Fig. REF . Let \(Z=(Z_1,...,Z_m)\)  and \(Y=(Y_1,...,Y_n)\)  be two vectors of data with model parameter vectors \(\varphi \)  and \(\theta \) . In our notation below we take the sample spaces to be \(Z_j\in \mathbb {R}^{d_z},\ j=1,...,m\) , \(Y_i\in \mathbb {R}^{d_y},\ i=1,...,n\) , \(\varphi \in \mathbb {R}^{p_\varphi }\)  and \(\theta \in \mathbb {R}^{p_\theta }\)  though this is not an essential restriction and our final example takes discrete data.
In Generalised Bayesian inference with a Gibbs posterior [1]}, [2]}, [3]}, [4]} we have a prior \(\pi _0(\theta ,\varphi )\)  (a density here) and a loss \(l(\varphi ,\theta ;Y,Z)\)  connecting the data and parameters, measuring how well the parameters agree with the data.
